Definition:Power (Algebra)/Integer/Knuth Notation

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Definition

In certain contexts in number theory, the symbol $\uparrow$ is used to denote the (usually) integer power operation:

$x \uparrow y := x^y$

This notation is usually referred to as Knuth (uparrow) notation.


Note that Knuth (uparrow) notation is right-associative, and so:

$x \uparrow y \uparrow z$

is interpreted as:

$x \uparrow \left({y \uparrow z}\right)$

Some authors prefer to retain the parenthesis.


Source of Name

This entry was named for Donald Ervin Knuth.